The miniature horse in this video has been reported as the tiniest one in Great Britain. It is actually a dwarf miniature horse.
Dwarfism is not uncommon in miniature horse but it is not desirable has it comes with health and keeping difficulties.
The dwarfism gene is recessive, meaning that you have to cross two horses carrying this gene to get a dwarf miniature horse. This is something that cannot be known ahead of time, unless one of the genitors already procreated a dwarf miniature horse.
It is stressed in this video that dwarfism comes with hindrances and thought it should not be sought after for the sake of competing for the record book gold medal in the smallest horse section.